Solve for x in the inequality (2x-1) / 3 > 1. Cite an axiom, definition or theorem at each step. Show the solution set on the number line.

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epsm79's profile pic

epsm79 | Middle School Teacher | (Level 1) eNoter

Posted on

(2x - 1) / 3 > 1 

multply 3 to both sides(multiplication property of inequality)            

2x - 1 > 3

add 1 to both sides(addition property of inequality)        

2x > 4

divide both sides by 2(dividion property of inequality)

x > 2

                                                          O------------------>

<-----|-----|-----|-----|-----|-----|-----|-----|-----|------->

        -4     -3     -2     -1      0      1       2      3      4

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

First, we'll subtract 1 both sides:

(2x-1)/3 - 1 > 0

We'll multiply 1 by 3:

(2x - 1 - 3)/3 > 0

We'll combine like terms within brackets:

(2x-4)/3 > 0

A fraction is positive if both, numerator and demominator, have the same sign.

Since the denominator of the fraction, namely 3, is positve, therefore, to keep the sense of the inequality, the numerator must be also positive:

2x - 4 > 0

We'll add 4 both sides, to isolate 2x to the left:

2x > 4

We'll divide by 2 both sides and the sense of inequality holds:

x > 4/2

x > 2

The values of x, for the inequality holds, belong to the opened interval (2 ; +`oo` ).

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